hierarchical modelling of last mile logistic distribution system

ORIGINAL ARTICLE

Hierarchical modelling of LastMile logistic distribution system

Tauseef Aized & Jagjit Singh Srai

Received: 13 January 2011 /Accepted: 25 September 2013 /Published online: 10 October 2013# Springer-Verlag London 2013

Abstract Last Mile logistic distribution system is the finalstep in business-to-customer supply chain which needs carefulinvestigation in order to efficiently and economically delivergoods to customers. This study is aimed at providing a con-ceptual planning approach of modelling a Last Mile systembased on hierarchy which is particularly useful in routingplanning of the system. The hierarchical modelling is imple-mented using the Petri net method which is suitable to theneeds of the system being a discrete event dynamical system.

Keywords Supply chain . LastMile logistic system .

Modelling

1 Introduction

A supply chain is as an integrated process in which a numberof various business entities like suppliers, manufacturers, dis-tributors and retailers work together in an effort to acquire rawmaterials, convert materials into final products and deliverthem to retailers and customers. The concept of supply chainemerged from a number of changes in the manufacturingenvironment, including the rising costs of manufacturing,the shrinking resources of manufacturing bases, the shortenedproduct life cycles and the globalization of market economies

[1]. During the last three decades, supply chain managementhas gained much attention because by coordinating the pro-duction, shipment and delivery of the goods required to meettheir business needs, organizations have been able to moreeasily meet the demands of their customers. In most supplychain operations, raw materials after passing through theprocessing industry and attaining the shape of finished goodsare stored in warehouses or distribution centres from wheretwomain options of distributing the goods are possible: firstly,the traditional system with supermarkets and retail shops andsecondly, a system with direct-to-consumer deliveries. TheLast Mile in the supply chain is considered as the last part ofthe supply chain for the direct-to-consumer market. In supplychain logistic operations, Last Mile refers to the last part ofphysical goods delivery process which involves a set of activ-ities that are necessary for the delivery process from the lasttransit point to the final drop point of the delivery chain. TheLast Mile is critical because it is responsible for the finaldelivery of products to customers and is typically a source ofhigh amount of costs of delivery chains. This paper focuses onthe Last Mile logistic distribution process and is organized insuch a way that Section 2 gives details of related work andcontribution of this paper. Section 3 explains LastMilemodel-ling, system configuration and hierarchical and Petri net-basedmodelling scheme, and conclusion is drawn in Section 4.

2 Related work and contribution

In order to effectively design, coordinate and manage supplychain systems, many methods and models have been devel-oped which mainly consist of deterministic, stochastic, eco-nomic and simulation modelling paradigms [1]. Among sup-ply chain management activities, one important concern islogistics and freight management. A review of urban freightstudies that have taken place in the UK over approximately a

T. AizedDepartment of Mechanical, Mechatronics and ManufacturingEngineering, UET, KSK Campus, Lahore, Pakistan

T. Aized (*)Institute for Manufacturing (IFM), University of Cambridge,Cambridge, UKe-mail: [email protected]

J. S. SraiCentre for International Manufacturing, Institute for Manufacturing(IFM), University of Cambridge, Cambridge, UK

Int J Adv Manuf Technol (2014) 70:1053–1061DOI 10.1007/s00170-013-5349-3

30-year period from the early 1970s to the present has beenpresented in [3] which covered both goods collection anddelivery and service vehicle activities. The significance ofelectronic commerce for freight transport, logistics and phys-ical distribution has been discussed in [9]. Russo and Comi[18] analysed existing studies relative to freight policies im-plemented at urban scale and proposed a general classificationof measures adopted at an urban scale with empirical analysisof results of proposed measures. The freight pipelinesdiscussed in [6] presented a novel way for the movement offreight transport and offered an alternative to conventionaltransport modes. Cidell [4] examined the suburbanization ofwarehousing and trucking activity in metropolitan areas usingGini indices as a measure of concentration. An analysis of theevolution of logistics pertaining to the core dimensions oftransport geography (flows, nodes/locations and networks) ispresented in [10], and the concept of logistical friction is alsointroduced to illustrate the inclusion of the multidimensionalnotion of impedance in integrated freight transport.

A comprehensive discussion on operational research-baseddynamic modelling is given in [15] and that on stochasticprogramming in transportation and logistics is in [16]. Ageneral modelling and algorithmic framework, based onmathematical programming techniques for the tactical plan-ning of freight transportation, was developed in [5] whichgenerated, evaluated and selected operating strategies by glob-ally considering the service network of the company and therouting of the freight under the double criteria of economicefficiency and service quality. A review of operational re-search models regarding intermodal freight transportation isgiven in [12] which emphasized intermodal over unimodaltransport modes. A marginal-cost-based framework was de-veloped in [14] to analyse the resulting trade-offs betweentravel distance and vehicle capacity utilization in the contextof freight carrier operations. Soehodho and Nahry [19] fo-cussed on traffic flow dependency within a freight distributionnetwork with the mathematical formulation of a minimumcost multicommodity flow (MCMF) problem. Traffic flowdependency was incorporated into the model by introducinga coefficient of speed, which was derived from the trafficassignment of ordinary traffic associated with the transpor-tation of the type of freight under consideration. A com-pilation of the solutions and initiatives that can be imple-mented by local administrations in order to improvefreight deliveries in urban environments is discussed in[13] from the point of view of urban communities andthe relation between freight transport and general urbantraffic. Russo and Comi [17] developed a model system inorder to support ex ante assessment of city logistic mea-sures which allowed to simulate the choices of eachdecision-maker involved in the urban freight transportand logistics and to investigate how the policies andmeasures can influence different choices.

Around the world, interest in urban and metropolitan goodsmovements is increasing since they account for a substantialshare of traffic in urban/metropolitan areas but there have beenonly few studies that considered the behaviour of the stake-holders in the Last Mile logistic area [20]. Although the LastMile system has different environmental, social and techno-logical issues, this study is aimed to examine routing planningof distribution system. This paper is focused on the Last Miledistribution system using hierarchical modelling concept im-plemented through Petri net. Previous work on the subjectdoes not deal the Last Mile logistic distribution network as adiscrete event hierarchical modelling paradigm. The advan-tage of dealing the Last Mile network as a discrete eventproblem, modelled through Petri net, is that it can effectivelyhandle routing planning of logistic network. Also, the Petri netmethod has the merit to accommodate any changes in model-ling network which usually arise from time to time, a featurecommonly known as scalability in discrete event modellingapproach. As discrete event systems grow, the modellingbecomes complex but Petri net has an ability to model grow-ing changes, that is, Petri nets especially higher classes of Petrinet like coloured Petri net are characteristically scalablemodels. Additionally, when models grow and become com-putationally complex and expensive, they need more andmore time to reach solutions. Coloured Petri net approach,being an advanced class of Petri net, has constructs like place,arc and transitions which can have mathematical functionsand hence can solve computationally complex problems inrelatively shorter time; if coupled with modern computationalcomputer process, more and more complex problems can besolved easily in shorter periods of time. This paper discussesthe downstream end of a single channel supply chain. Due tothe involvement of customers, this end of supply chains isdifficult to handle and therefore should be carefully modelled.As the preferences, choices and demand patterns vary with thepassage of time, hence the downstream side of supply chainscauses a lot of uncertainties and variations which may prop-agate towards the upstream side of the chain. Consequently,modelling the downstream side of supply chain due to thepresence of uncertainties is a challenging task.

3 Last Mile modelling

Last Mile focuses on the period when parcels leave the trans-portation system, that is, the last step in the delivery process.Usually, a parcel is bought to the recipient’s home/office or itcan also be stored until the recipient picks it up or forwarded toanother address. It is the link between an online orderingprocess and physical product delivery [7]. It involves a setof activities that are necessary for the delivery process fromthe last transit point to the final drop point of the deliverychain. The Last Mile is the last stretch of a business-to-

1054 Int J Adv Manuf Technol (2014) 70:1053–1061

consumer parcel delivery to the final consignee who has totake reception of the goods at home or at a cluster/collectionpoint. The Last Mile is considered one of the most expensiveparts of the supply chains and accounts for 13% up to 75% ofthe total supply chain costs [8]. Among the problems encoun-tered in designing Last Mile are the high degree of faileddeliveries which yields extra costs, a high degree of emptyrunning of vehicles and a low volume of delivery goods.These problems call for an efficient routing planning in orderto generate reasonable profit margins necessary to run thesystem smoothly.

3.1 System configuration

The Last Mile system configuration in relation to a partialsupply chain considered in this study is shown in Fig. 1. Inorder to focus the Last Mile operations, the components ofsupply chain before production facility, that is factory, are notshown. In this system, the customer places an order to theretailer or a “parcel source” (e.g. friends, relatives, etc.). Whilethe parcel is being processed, there can be also an informationexchange between the transportation service provider and thecustomer (e.g. parcel tracking, notice of expected arrival, etc.).The shipping unit is getting processed (e.g. factory, ware-houses, cross-docking hubs, sorting, different types of trans-portation, etc.) till it arrives at the defined urban area. Cross-docking is the process of rehandling freight from inboundtrucks and loading it to outbound vehicles [2] .

The information and material flow among different com-ponents of the system are shown in Fig. 1. The Last Milesystem comprising of transit point, drop point and customer isfurther elaborated in Fig. 2.

The transit point is the last cross-docking point within thesupply chain whichmay be a consolidation centre, distributionhub or a retailer outlet. Consolidation, in the context of freight

transport, refers to the reduction in the number of vehiclesoperating with part or full load. This is achieved by combiningdelivery orders for the same or similar location for at least partof the journey. Urban consolidation centres (UCCs) are oper-ated by a single, major logistic operator who is responsible forrunning the centre and making the final deliveries. Freightconsolidation centres (FCCs) are distribution warehouses,situated close to town centre, shopping or construction site,at which loads are consolidated and delivered to the target arearesulting in fewer journeys. The important characteristic ofconsolidation centres is that shipping units are cross-dockingprocesses to fulfil the last mile in the way it satisfies theinvolved stakeholders (e.g. increase load factor, reduce trafficin urban area, etc.). Hubs commonly serve as consolidation,switching and sorting centres and allow for the replacement ofdirect connections between all nodes with fewer, indirectconnections. However, the main difference from consolida-tion centres is that distribution hubs are, in general, onlydistributing the goods from one or a few defined origins.The retailer outlet is a good supply facility that directly de-livers to the customer. The retailer outlet is also placed in theurban area and provides in general the possibility of in-storeshopping for the customer. The roll-out logistics providers areresponsible for delivery from the last transit point to thespecific drop point. In general, the roll-out logistics operatesfrom one specific hub and delivers the parcels to the assignedurban area. The drop point is the place where the roll-outlogistics service provider drops the parcel and the customerreceives or picks up the shipping unit. There can be differentpossibilities for drop points like collection point, neighbour,etc. All delivery options that are designated to ship the freightunits not to the customer’s home are grouped into a termcalled “collection point”. This also involves that the customerneeds to go to the collection point to pick up the parcel. Theterm “neighbour” summarizes all the events when the parcel is

Retailer

Factory

Parcelsource

Or

Warehouse

Transit point

Hub 1

Hub n

Drop point Customer

Informationmanagement

Simplified flow model (one layer model)

Material flow Information flow

Defined urbanarea of the last

mile system

Fig. 1 Last Mile operations in partial supply chain

Int J Adv Manuf Technol (2014) 70:1053–1061 1055

not delivered to its set destination and be handed over to athird party that is close to the customer. In home delivery, thegoods are being delivered to the home of the customer. Thisincludes home delivery service with/without time windowas well as home delivery service to the home-unattendedreception box.

3.2 Hierarchical modelling of the Last Mile system

The Last Mile system is confined to a specific geographicallocation in which transit point, drop point and customers arepresent. In order to define a specific Last Mile region, manyfactors are taken into consideration which include distancebetween transit points of adjacent regions, local infrastructureand regulations, road network, traffic intensity, parking space,congestion, tolls and taxes, etc. There are certain indicatorsrelated to residents which need careful consideration whendefining a Last Mile region. These indicators are quantitativelike number of customers and number of houses in the region,socio-economic which includes purchasing power of residentsand socio-demographic like age of householders and type,variability and prediction of demand pattern. Based on thesefactors, the customer density ratio, defined as the expectedcustomers in a specific area, can be calculated, which is one ofcritical factors in designing a Last Mile system.

A three-layered hierarchical model is developed in thisstudy for planning the Last Mile region. These are institution-al, industrial and customer layers. The top layer called insti-tutional layer gives the total perspective of the system inwhich four transit points have been assumed, although thenumbers of transit points may vary from case to case depend-ing on the design considerations of the Last Mile system. Thetrucks deliver goods to these transit points and return. Thenext layer is called industrial layer, and transit points are

available in both institutional and industrial layers as bothlayers are actually connected to each other at these points.From the transit points, vans pick up the goods and stuff andmove into the industrial layer of the Last Mile region. The vanhas to serve attended points, unattended points and con-sumer’s house which is available in the lowest hierarchicallayer called consumer layer. The house in the consumer layeris the destination point of the stuff, but the consumer may haveto visit attended and unattended drop points if he/she wishes tohave his stuff dropped there. This three-layered hierarchicalmodel is shown in Fig. 3.

3.3 Petri net modelling of the Last Mile system

The Last Mile transport system is a discrete event dynamical(DEDS) system, which is asynchronous, parallel and event-driven in nature. The routing planning of the Last Mile systemcan be carried out with the Petri net method which is a genericmethod for DEDSmodelling. A DEDS can be characterized byevents and conditions. A Petri net consists of places, transitionsand directed arcs represented by circles, rectangular bars andarrows, respectively. Arcs run between places and transitions.Places may carry a number of tokens, and a distribution oftokens over the places of a net is called a marking. Transitionsact on input tokens by a process known as firing or occurring. Atransition can fire or occur if it is enabled, i.e. there are tokens inevery input place.When a transition fires or occurs, it consumesthe tokens from its input places, performs some activity andplaces a specified number of tokens which may vary from zeroto any definite number into each of its output places. Theconditions of a Last Mile system, being a DEDS, may bedescribed by places, events by transitions, relations betweenevents and conditions by arcs and holding of conditions bytokens in places. The occurrences of events are described by

Defined urban area

Drop point

Express delivery logistics

Consolidationcentre

Transit point

Ro

ll-o

ut

log

isti

cs

Inboundlogistics

Privatecustomer

Distribution hub

Retailer outlet

Collection point

Customer home

Neighbor

Fig. 2 Last Mile logistic system


firing of transitions which remove tokens from input places andadd tokens to output places, and the behaviour of a system isdescribed by firing of transitions and movements of tokens.Places, transitions and tokens must be assigned a meaning forproper interpretation of a model. In the Last Mile systems,places may represent resources like transportation means, thatis, trucks/vans, etc., and the existence of one or more tokens in aplace represents the availability of a particular resource, whileno token indicates that the resource is unavailable. A transitionfiring represents an activity or process execution, for instance, atransportation process. Places and transitions together representconditions and precedence relationships in the Last Mile sys-tem’s operation. Due to a large number of resources, conditionsand activities, the Petri net model can be of a big size with a lotof places, transitions, arcs and their allied constructs in a prac-tical Last Mile system, and it becomes extremely tedious tohandle and comprehend such a big modelling net. This problemcan be solved using a higher class of Petri net called colouredPetri net (CPN) which can compactly handle bigger modellingnets. This study uses the formal definition of CPN given in [11].A hierarchical CPN is a tuple HCPN=(S, SN, SA, PN, PT, PA,FS, FT, PP) satisfying the following requirements:

1. S is a finite set of pages such that:Each page s∈S is a non-hierarchical CPN:

CPN ¼ ∑s; Ps;Ts;As;Ns;Cs;Gs;Es; Isð Þ

(The non-hierarchical CPN is defined in [11].)The sets of net elements are pairwise disjoint:

∀s1; s2∈S : s1≠s2⇒ Ps1∪Ts1∪As1ð Þ∩ Ps2∪Ts2∪As2ð Þ ¼ � �:½

2. SN⊆T is a set of substitution nodes.3. SA is a page assignment function. It is defined from SN

into S such that:No page is a sub page of itself:

s0s1…sn∈S*��n∈Nþ ∧s0 ¼ sn∧∀k∈1…n : sk∈SA SNsk−1ð Þ

n o

¼ � :

4. PN⊆P is a set of port nodes.5. PT is a port-type function. It is defined from PN into {in,

out, i/o, general}.PA is a port assignment function, FS⊆Ps is a finite set

of fusion sets, FT is a fusion-type function and PP∈SMs isa multiset of prime pages. For details of PA, FS and FT,we refer to [13].

The model is developed using CPN Tools which is a CPN-based program developed on the basis of CPN ML language.The CPNML language is derived from StandardMLwhich isa general-purpose language. The Last Mile logistic distribu-tion system has beenmodelled byCPN Tools which is capableto simulate and validate the system. Figures 4, 5 and 6 showthe snapshots of models taken from CPN Tools.

1

Defined Urban Area

OR

TruckTransitpointarrival

Transitpoint

outwardsVan

Droppoint

Customerhome

1

2

3

Institutional Layer

Industrial Layer

Key

Drop point (Consumer home)

Drop point (attendant)

Drop point (unattendant)

Transit point

Transportation vehicle

The granularity off low (three layer model)

Consumer Layer

Fig. 3 Hierarchical modelling of the Last Mile system


stuff(4)

stuff(3)

stuff(2)stuff(1)

(t,tc)(t,tc)

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movingto 4

[t=Truck(4)andalsotc=loaded]

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[tc=unloaded]

Ready toreturn 2

unloading 2

[t=Truck(2)andalsotc=loaded]

returningfrom 3

[ tc=unloaded]

[(t=Truck(2) orelse t=Truck(4))andalso (tc=loaded)]

ready toreturn 3 unloading 3

[t=Truck(3) andalsotc=loaded]

movingto 3


returningfrom 1

[tc=unloaded]

Ready toreturn 1

unloading1


[(t=Truck(1) orelse t=Truck(3))andalso (tc=loaded)]

stuff_4_available

Fusion 4Stuff

Stuff_3_available

Fusion 3Stuff

Stuff_2_available

Fusion 2

Stuff

Stuff_1_available

Fusion 1Stuff

stuff_4

Transit_Pointstuff_2

Transit_Point

stuff 3

Transit_Point

Stuff_1

Transit_Point

Trucks moving toInstitutional Layer

1`(Truck(1), loaded)++1`(Truck(2),loaded)++1`(Truck(3), loaded)++1`(Truck(4), loaded)

Transit_Point

Point 4

Transit_Point

Point 3

Transit_Point

Point 2

Transit_Point

Point 1

Transit_Point

Fusion 1 Fusion 2

Fusion 3Fusion 4

Fig. 4 Institutional layer of the coloured Petri net model

v

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empty

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(s,v) (s,v) v

empty

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(s,v)(s,v)(s,v)

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moving11

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moving8 moving7 moving 6 stuff laoding 4

moving6

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moving3moving2moving1stuffloading 1

approaching8 Stuff_condition

approaching7Stuff_condition

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approaching2

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stuff_3_available

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House 2Fusion 16

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unattended point 2Fusion 15

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attended point 2Fusion 14

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van4

Vansvan2

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stuff loaded 2

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Van3

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House 4Fusion 13 Stuff_condition

reached 4

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unattended point 4Fusion 12

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reached point 2

Vans

attended point 4Fusion 11

Stuff_condition

stuff loaded 4

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Stuff forHouse 3

Fusion 10Stuff_condition

unattendedpoint 3

Fusion 9 Stuff_condition

unattendedpoint 1

Fusion 6

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attendedpoint 1


stuff loaded3Stuff_condition

Stuff forHouse1


reachedpoint 3

Vans

attendedpoint 3


van1

1`van(1)

Vans

stuffloaded 1

Stuff_condition

Fusion 8

Fusion 7Fusion 5 Fusion 6

Fusion 9

Fusion 10

Fusion 11Fusion 12Fusion 13

Fusion 14

Fusion 15

Fusion 16

Fusion 2

Fusion 1

Fusion 3

Fusion 4

Fig. 5 Industrial layer of the coloured Petri net model


All three layers of the model, that is, institutional, industrialand consumer, are connected through hierarchical relation-ships using a construct of CPN Tools called fusion place set[11]. The model developed is conceptual in nature as the aimof this study is to elaborate a methodology based on Petri netfor hierarchical modelling of the LastMile system. This modelassumes four transit points in a defined geographical regionwhere trucks arrive, offload and return. The stuff offloaded isloaded on a van which visits one attended and unattended droppoint to deliver goods and then approaches a house for a housedelivery. After serving one drop point, the van moves to servethe next drop points in a similar way, and after completing allfour drop points, it returns to its original location, that is, thefirst drop point in the industrial layer. This scheme of pickingand dropping material is hypothetical but can be used to addspecific conditions and constraints required in any particularLast Mile system. The requirements of the system may in-clude time and capacity specifications of trucks deliveringgoods in the Last Mile system; scheduling, routing and num-ber of vans aimed at delivering the goods in the region; thescheme of delivering goods; and other related conditions. Theconceptual hierarchical modelling of the Last Mile system andits implementation using Petri net is a convenient method foranalysing the system under consideration. Such a modellingmethod can accommodate any changes which may arise any-time in the Last Mile logistic distribution system; hence, thecoloured Petri net modelling method is scalable in its formatand is a suitable technique to incorporate any changes in thesystem.

Places and transitions in Figs. 4, 5 and 6, that is, institu-tional, industrial and customers layers, are named descriptive-ly. Table 1 shows the places/transitions and their description inthe institutional layer where similar explanation is assumedfor the industrial and customer layers.

The conceptual modelling results generated by thecoloured Petri net method using CPN Tools presented in thispaper have been validated using another class of Petri netcalled high-level Petri net which has been modelled andsimulated using ALPHA/Sim tools. The use of high-levelPetri net through ALPHA/Sim for validation purpose has

Packet(2)Packet(2)

Packet(2)

(s,v)

(s,v)

(s,v)

pp

pp

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pp

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p (s,v)

delivering 2

for attendedpoint 2

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for attendedpoint 4

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for attendedpoint 3

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House 2 person

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stuff forHouse 4


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AttendedPoint 4

Fusion 11

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House 4 person

1`person(4)

Person

UnattendedPoint 3


AttendedPoint 3


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Fusion 10

Stuff_condition


Packet

House 3 person

1`person(3)

Person

UnattendedPoint 1


House 1 person

1`person(1)

Person

Attendedpoint 1



Packet

Stuff forHouse 1

Fusion 7 Stuff_conditionFusion 7

Fusion 5Fusion 6

Fusion 10

Fusion 8

Fusion 9

Fusion 15

Fusion 11

Fusion 12

Fusion 13

Fusion 14

Fusion 16

Fig. 6 Customer layer of the coloured Petri net model

Table 1 Institutional layer places and transitions description

Place Description

Trucks moving to theinstitutional layer

Trucks are approaching the institutional layerof the Last Mile system

Points 1, 2, 3 and 4 Geographical distribution of four points

Stuff 1, 2, 3 and 4 Unloaded stuff at points 1, 2, 3 and 4

Stuff 1, 2, 3 and 4available

Stuff 1, 2, 3 and 4 available for transportationto the industrial layer

Transition Descriptions

Unloadings 1, 2, 3 and 4 Trucks are being unloaded at points 1, 2, 3and 4

Ready to return 1, 2, 3and 4

Trucks are ready after unloading at points 1,2, 3 and 4

Returning from 1, 2, 3and 4

Trucks are returning from points 1, 2, 3 and 4and moving out of the institutional layer


revealed that coloured Petri net is more compact and scalable,hence more suitable for the Last Mile logistic distributionsystem.

3.4 Case example

A case example has been developed to demonstrate thecoloured Petri net-based modelling of the Last Mile distribu-tion system. The number of vans in the customer layer hasbeen increased from 1 to 4. In the first case, there is only onevan which is serving the entire customer layer. T1, T2, T3 andT4 are the times which are required when the delivery stuff isdistributed in customer 1, 2, 3 and 4 regions. The van movesfrom customer region 1 to region 3, from where it moves toregion 4 and finally to region 2. The stuff numbers 1, 2 and 3denote stuff delivered at the attended point, the unattendedpoint and the customer house point, respectively. Time ismeasured in dimensionless time units while simulating themodel. In case #1, the stuff delivery time is increasing as thevan moves from the first to the last customer region. Thenumber of vans has been increased to 2 in case #2 in such away that the first van serves customer regions 1 and 3 and thesecond van serves regions 4 and 2. The stuff delivery timeshave improved as T1 and T4 and also T3 and T2 becomeequal. The delivery time can further be improved by addinganother van in the system as is shown in case #3 where thereare independent vans for regions 1 and 3 but one van forregions 4 and 2 which first serves region 4 and then region2. In the last case (case #4), all customer regions have separatevans, and hence, stuff delivery time becomes equal. The keyperformance metrics for the Last Mile logistic distributionsystem is the time required to deliver stuff to its specifieddestination in this study. Another associated measure withoverall time required to deliver stuff is resource (vans in thisstudy) utilization which can be measured by calculating the

time for which each van is in working (loading, unloading,moving, etc.) condition compared with the overall time periodfor which the logistic distribution system is studied. Althoughstuff delivery time is improved by adding more vans in thesystem, it should be noted that van utilization times are boundto decrease along with an increase in capital and overalllogistic distribution system expenses. Van utilization timescan be measured by adding coloured Petri net modellingconstructs in CPN Tools. Table 2 shows a decrease in timeto deliver stuff with an increase in the number of vans, but thistime decrease is directly linked with poor utilization of vans,and hence, the Last Mile logistic distribution system must befurther explored using CPN Tools in order to achieve a trade-off between delivery times and van utilization times.

4 Conclusion

LastMile is considered one important step in supply chain andbusiness-to-customer paradigms and is responsible for effi-cient and economical final delivery of goods to customers.This study has addressed the modelling issue of the Last Milesystem through the development of a hierarchical modellingimplemented through the Petri net method. The proposedscheme is suitable for routing and congestion planning ofdelivery goods in a defined geographical location. The studycan be furthered according to particular requirements of aparticular Last Mile logistic system. This research will beextended to incorporate other related technological, en-vironmental and social issues encountered in the logisticdistribution system.

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Table 2 Last Mile simulation results

Stuff number T1 T3 T4 T2

Case #1 (number of vans=1) 1 5 12 19 26

2 7 14 21 28

3 9 16 23 30


2 7 14 7 14

3 9 16 9 16


2 7 7 7 14

3 9 9 9 16


2 7 7 7 7

3 9 9 9 9


http://dx.doi.org/10.1016/j.jtrangeo.2010.05.004

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http://dx.doi.org/10.1016/%20j.retrec.%202010.11.011

http://dx.doi.org/10.1016/%20j.retrec.%202010.11.011

hierarchical modelling of last mile logistic distribution system

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